{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KF Basics - Part I\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction\n",
    "#### What is the need to describe belief in terms of PDF's?\n",
    "This is because robot environments are stochastic. A robot environment may have cows with Tesla by side. That is a robot and it's environment cannot be deterministically modelled(e.g as a function of something like time t). In the real world sensors are also error prone, and hence there'll be a set of values with a mean and variance that it can take. Hence, we always have to model around some mean and variances associated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### What is Expectation of a Random Variables?\n",
    " Expectation is nothing but an average of the probabilites\n",
    " \n",
    "$$\\mathbb E[X] = \\sum_{i=1}^n p_ix_i$$\n",
    "\n",
    "In the continous form,\n",
    "\n",
    "$$\\mathbb E[X] = \\int_{-\\infty}^\\infty x\\, f(x) \\,dx$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4000000000000001\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "x=[3,1,2]\n",
    "p=[0.1,0.3,0.4]\n",
    "E_x=np.sum(np.multiply(x,p))\n",
    "print(E_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### What is the advantage of representing the belief as a unimodal as opposed to multimodal?\n",
    "Obviously, it makes sense because we can't multiple probabilities to a car moving for two locations. This would be too confusing and the information will not be useful."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance, Covariance and Correlation\n",
    "\n",
    "#### Variance\n",
    "Variance is the spread of the data. The mean does'nt tell much **about** the data. Therefore the variance tells us about the **story** about the data meaning the spread of the data.\n",
    "\n",
    "$$\\mathit{VAR}(X) = \\frac{1}{n}\\sum_{i=1}^n (x_i - \\mu)^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0224618077401504"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=np.random.randn(10)\n",
    "np.var(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Covariance\n",
    "\n",
    "This is for a multivariate distribution. For example, a robot in 2-D space can take values in both x and y. To describe them, a normal distribution with mean in both x and y is needed.\n",
    "\n",
    "For a multivariate distribution, mean $\\mu$ can be represented as a matrix, \n",
    "\n",
    "$$\n",
    "\\mu = \\begin{bmatrix}\\mu_1\\\\\\mu_2\\\\ \\vdots \\\\\\mu_n\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "\n",
    "Similarly, variance can also be represented.\n",
    "\n",
    "But an important concept is that in the same way as every variable or dimension has a variation in its values, it is also possible that there will be values on how they **together vary**. This is also a measure of how two datasets are related to each other or **correlation**.\n",
    "\n",
    "For example, as height increases weight also generally increases. These variables are correlated. They are positively correlated because as one variable gets larger so does the other.\n",
    "\n",
    "We use a **covariance matrix** to denote covariances of a multivariate normal distribution:\n",
    "$$\n",
    "\\Sigma = \\begin{bmatrix}\n",
    "  \\sigma_1^2 & \\sigma_{12} & \\cdots & \\sigma_{1n} \\\\\n",
    "  \\sigma_{21} &\\sigma_2^2 & \\cdots & \\sigma_{2n} \\\\\n",
    "  \\vdots  & \\vdots  & \\ddots & \\vdots  \\\\\n",
    "  \\sigma_{n1} & \\sigma_{n2} & \\cdots & \\sigma_n^2\n",
    " \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "**Diagonal** - Variance of each variable associated. \n",
    "\n",
    "**Off-Diagonal** - covariance between ith and jth variables.\n",
    "\n",
    "$$\\begin{aligned}VAR(X) = \\sigma_x^2 &=  \\frac{1}{n}\\sum_{i=1}^n(X - \\mu)^2\\\\\n",
    "COV(X, Y) = \\sigma_{xy} &= \\frac{1}{n}\\sum_{i=1}^n[(X-\\mu_x)(Y-\\mu_y)\\big]\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.08868895, 0.05064471, 0.08855629],\n",
       "       [0.05064471, 0.06219243, 0.11555291],\n",
       "       [0.08855629, 0.11555291, 0.21534324]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=np.random.random((3,3))\n",
    "np.cov(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Covariance taking the data as **sample** with $\\frac{1}{N-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.1571437 , -0.00766623],\n",
       "       [-0.00766623,  0.13957621]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_cor=np.random.rand(1,10)\n",
    "y_cor=np.random.rand(1,10)\n",
    "np.cov(x_cor,y_cor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Covariance taking the data as **population** with $\\frac{1}{N}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.14142933, -0.0068996 ],\n",
       "       [-0.0068996 ,  0.12561859]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cov(x_cor,y_cor,bias=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussians \n",
    "\n",
    "#### Central Limit Theorem\n",
    "\n",
    "According to this theorem, the average of n samples of random and independent variables tends to follow a normal distribution as we increase the sample size.(Generally, for n>=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  4.,  9., 12., 12., 20., 16., 16.,  4.,  6.]),\n",
       " array([5.30943011, 5.34638597, 5.38334183, 5.42029769, 5.45725355,\n",
       "        5.49420941, 5.53116527, 5.56812114, 5.605077  , 5.64203286,\n",
       "        5.67898872]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "a=np.zeros((100,))\n",
    "for i in range(100):\n",
    "    x=[random.uniform(1,10) for _ in range(1000)]\n",
    "    a[i]=np.sum(x,axis=0)/1000\n",
    "plt.hist(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gaussian Distribution\n",
    "A Gaussian is a *continuous probability distribution* that is completely described with two parameters, the mean ($\\mu$) and the variance ($\\sigma^2$). It is defined as:\n",
    "\n",
    "$$ \n",
    "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\big [{-\\frac{(x-\\mu)^2}{2\\sigma^2} }\\big ]\n",
    "$$\n",
    "Range is $$[-\\inf,\\inf] $$\n",
    "\n",
    "\n",
    "This is just a function of mean($\\mu$) and standard deviation ($\\sigma$) and what gives the normal distribution the charecteristic **bell curve**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.mlab as mlab\n",
    "import math\n",
    "import scipy.stats\n",
    "\n",
    "mu = 0\n",
    "variance = 5\n",
    "sigma = math.sqrt(variance)\n",
    "x = np.linspace(mu - 5*sigma, mu + 5*sigma, 100)\n",
    "plt.plot(x,scipy.stats.norm.pdf(x, mu, sigma))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Why do we need Gaussian distributions?\n",
    "Since it becomes really difficult in the real world to deal with multimodal distribution as we cannot put the belief in two seperate location of the robots. This becomes really confusing and in practice impossible to comprehend. \n",
    "Gaussian probability distribution allows us to drive the robots using only one mode with peak at the mean with some variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Properties\n",
    "\n",
    "**Multiplication**\n",
    "\n",
    "\n",
    "For the measurement update in a Bayes Filter, the algorithm tells us to multiply the Prior P(X_t) and measurement P(Z_t|X_t) to calculate the posterior:\n",
    "\n",
    "$$P(X \\mid Z) = \\frac{P(Z \\mid X)P(X)}{P(Z)}$$\n",
    "\n",
    "Here for the numerator,  $P(Z \\mid X),P(X)$ both are gaussian.\n",
    "\n",
    "$N(\\mu_1, \\sigma_1^2)$ and $N(\\mu_2, \\sigma_2^2)$ are their mean and variances.\n",
    "\n",
    "New mean is \n",
    "\n",
    "$$\\mu_\\mathtt{new} = \\frac{\\mu_1 \\sigma_2^2 + \\mu_2 \\sigma_1^2}{\\sigma_1^2+\\sigma_2^2}$$\n",
    "New variance is\n",
    "$$\\sigma_\\mathtt{new} = \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New mean is at:  5.0\n",
      "New variance is:  1.0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.mlab as mlab\n",
    "import math\n",
    "mu1 = 0\n",
    "variance1 = 2\n",
    "sigma = math.sqrt(variance1)\n",
    "x1 = np.linspace(mu1 - 3*sigma, mu1 + 3*sigma, 100)\n",
    "plt.plot(x1,scipy.stats.norm.pdf(x1, mu1, sigma),label='prior')\n",
    "\n",
    "mu2 = 10\n",
    "variance2 = 2\n",
    "sigma = math.sqrt(variance2)\n",
    "x2 = np.linspace(mu2 - 3*sigma, mu2 + 3*sigma, 100)\n",
    "plt.plot(x2,scipy.stats.norm.pdf(x2, mu2, sigma),\"g-\",label='measurement')\n",
    "\n",
    "\n",
    "mu_new=(mu1*variance2+mu2*variance1)/(variance1+variance2)\n",
    "print(\"New mean is at: \",mu_new)\n",
    "var_new=(variance1*variance2)/(variance1+variance2)\n",
    "print(\"New variance is: \",var_new)\n",
    "sigma = math.sqrt(var_new)\n",
    "x3 = np.linspace(mu_new - 3*sigma, mu_new + 3*sigma, 100)\n",
    "plt.plot(x3,scipy.stats.norm.pdf(x3, mu_new, var_new),label=\"posterior\")\n",
    "plt.legend(loc='upper left')\n",
    "plt.xlim(-10,20)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Addition**\n",
    "\n",
    "The motion step involves a case of adding up probability (Since it has to abide the Law of Total Probability). This means their beliefs are to be added and hence two gaussians. They are simply arithmetic additions of the two.\n",
    "\n",
    "$$\\begin{gathered}\\mu_x = \\mu_p + \\mu_z \\\\\n",
    "\\sigma_x^2 = \\sigma_z^2+\\sigma_p^2\\, \\square\\end{gathered}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New mean is at:  15\n",
      "New variance is:  2\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.mlab as mlab\n",
    "import math\n",
    "mu1 = 5\n",
    "variance1 = 1\n",
    "sigma = math.sqrt(variance1)\n",
    "x1 = np.linspace(mu1 - 3*sigma, mu1 + 3*sigma, 100)\n",
    "plt.plot(x1,scipy.stats.norm.pdf(x1, mu1, sigma),label='prior')\n",
    "\n",
    "mu2 = 10\n",
    "variance2 = 1\n",
    "sigma = math.sqrt(variance2)\n",
    "x2 = np.linspace(mu2 - 3*sigma, mu2 + 3*sigma, 100)\n",
    "plt.plot(x2,scipy.stats.norm.pdf(x2, mu2, sigma),\"g-\",label='measurement')\n",
    "\n",
    "\n",
    "mu_new=mu1+mu2\n",
    "print(\"New mean is at: \",mu_new)\n",
    "var_new=(variance1+variance2)\n",
    "print(\"New variance is: \",var_new)\n",
    "sigma = math.sqrt(var_new)\n",
    "x3 = np.linspace(mu_new - 3*sigma, mu_new + 3*sigma, 100)\n",
    "plt.plot(x3,scipy.stats.norm.pdf(x3, mu_new, var_new),label=\"posterior\")\n",
    "plt.legend(loc='upper left')\n",
    "plt.xlim(-10,20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Example from:\n",
    "#https://scipython.com/blog/visualizing-the-bivariate-gaussian-distribution/\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# Our 2-dimensional distribution will be over variables X and Y\n",
    "N = 60\n",
    "X = np.linspace(-3, 3, N)\n",
    "Y = np.linspace(-3, 4, N)\n",
    "X, Y = np.meshgrid(X, Y)\n",
    "\n",
    "# Mean vector and covariance matrix\n",
    "mu = np.array([0., 1.])\n",
    "Sigma = np.array([[ 1. , -0.5], [-0.5,  1.5]])\n",
    "\n",
    "# Pack X and Y into a single 3-dimensional array\n",
    "pos = np.empty(X.shape + (2,))\n",
    "pos[:, :, 0] = X\n",
    "pos[:, :, 1] = Y\n",
    "\n",
    "def multivariate_gaussian(pos, mu, Sigma):\n",
    "    \"\"\"Return the multivariate Gaussian distribution on array pos.\n",
    "\n",
    "    pos is an array constructed by packing the meshed arrays of variables\n",
    "    x_1, x_2, x_3, ..., x_k into its _last_ dimension.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    n = mu.shape[0]\n",
    "    Sigma_det = np.linalg.det(Sigma)\n",
    "    Sigma_inv = np.linalg.inv(Sigma)\n",
    "    N = np.sqrt((2*np.pi)**n * Sigma_det)\n",
    "    # This einsum call calculates (x-mu)T.Sigma-1.(x-mu) in a vectorized\n",
    "    # way across all the input variables.\n",
    "    fac = np.einsum('...k,kl,...l->...', pos-mu, Sigma_inv, pos-mu)\n",
    "\n",
    "    return np.exp(-fac / 2) / N\n",
    "\n",
    "# The distribution on the variables X, Y packed into pos.\n",
    "Z = multivariate_gaussian(pos, mu, Sigma)\n",
    "\n",
    "# Create a surface plot and projected filled contour plot under it.\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, rstride=3, cstride=3, linewidth=1, antialiased=True,\n",
    "                cmap=cm.viridis)\n",
    "\n",
    "cset = ax.contourf(X, Y, Z, zdir='z', offset=-0.15, cmap=cm.viridis)\n",
    "\n",
    "# Adjust the limits, ticks and view angle\n",
    "ax.set_zlim(-0.15,0.2)\n",
    "ax.set_zticks(np.linspace(0,0.2,5))\n",
    "ax.view_init(27, -21)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a 3D projection of the gaussians involved with the lower surface showing the 2D projection of the 3D projection above. The innermost ellipse represents the highest peak, that is the maximum probability for a given (X,Y) value.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "** numpy einsum examples **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]\n",
      " [20 21 22 23 24]]\n",
      "[0 1 2 3 4]\n",
      "[[0 1 2]\n",
      " [3 4 5]]\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(25).reshape(5,5)\n",
    "b = np.arange(5)\n",
    "c = np.arange(6).reshape(2,3)\n",
    "print(a)\n",
    "print(b)\n",
    "print(c)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 30,  80, 130, 180, 230])"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#this is the diagonal sum, i repeated means the diagonal\n",
    "np.einsum('ij', a)\n",
    "#this takes the output ii which is the diagonal and outputs to a\n",
    "np.einsum('ii->i',a)\n",
    "#this takes in the array A represented by their axes 'ij' and  B by its only axes'j' \n",
    "#and multiples them element wise\n",
    "np.einsum('ij,j',a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 22, 76])"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.arange(3).reshape(3,1)\n",
    "B = np.array([[ 0,  1,  2,  3],\n",
    "              [ 4,  5,  6,  7],\n",
    "              [ 8,  9, 10, 11]])\n",
    "C=np.multiply(A,B)\n",
    "np.sum(C,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 22, 76])"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = np.array([0,1,2])\n",
    "E = np.array([[ 0,  1,  2,  3],\n",
    "              [ 4,  5,  6,  7],\n",
    "              [ 8,  9, 10, 11]])\n",
    "\n",
    "np.einsum('i,ij->i',D,E)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x139196438>"
      ]
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAADXNJREFUeJzt3durpXUdx/HPZ8/BGZhxvFAR3FMjFYhkYAwWeVF4CKtBbwpKEsSLfZOgYEg2/0AQdICK2FgQJEhkUUQHR9KLLhR10sJDoTLqSKIRpFAog98u1t659551eA6/Zz1rfZ/3C4S91n727/nxMLz5+VuHxxEhAEAeK31PAABQFmEHgGQIOwAkQ9gBIBnCDgDJEHYASIawA0AyhB0AkiHsAJDM7j5Oundlf+zfdbCPUwPA0nrzzBv/jIgLZh3XS9j37zqoT5z/hT5ODQBL6/ev/eClKsexFQMAyRB2AEiGsANAMoQdAJIh7ACQDGEHgGQIOwAkQ9gBIBnCDgDJEHYASIawA0AyhB0AkiHsAJAMYQeAZIqF3fYu23+2/ZtSYwIA6iu5Yr9d0rMFxwMANFAk7LZXJX1O0j0lxgMANFdqxf4dSXdJerfQeACAhlqH3fYxSa9HxBMzjluz/bjtx995979tTwsAmKDEiv0qSTfYPiXpPklX2/7pzoMiYj0ijkbE0b0r+wucFgAwTuuwR8TdEbEaEUckfVHSHyPiy61nBgBohPexA0Ayu0sOFhEPS3q45JgAgHpYsQNAMoQdAJIh7ACQDGEHgGQIOwAkQ9gBIBnCDgDJEHYASIawA0AyhB0AkiHsAJAMYQeAZAg7ACRD2AEgGcIOAMkQdgBIhrADQDKEHQCSIewAkAxhB4BkCDsAJEPYASAZwg4AyRB2AEiGsANAMoQdAJIh7ACQDGEHgGQIOwAkQ9gBIBnCDgDJEHYASIawA0AyhB0AkiHsAJBM67DbPmz7IdvP2H7a9u0lJgYAaGZ3gTHOSLozIk7aPijpCdsnIuKZAmMDAGpqvWKPiH9ExMmNn9+S9Kyki9uOCwBopugeu+0jkq6Q9GjJcQEA1ZXYipEk2T4g6X5Jd0TEm2N+vyZpTZL2rRwodVoAwA5FVuy292gU9Xsj4hfjjomI9Yg4GhFH967sL3FaAMAYJd4VY0k/kvRsRHyr/ZQAAG2UWLFfJelmSVfbfnLjv88WGBcA0EDrPfaI+JMkF5gLAKAAPnkKAMkQdgBIhrADQDKEHQCSIewAkAxhB4BkCDsAJEPYASAZwg4AyRB2AEiGsANAMoQdAJIpdqMNAGjqnUtXW4+x97nTBWaSA2EH0LkS4a56DgJP2AEUNI+AV53DkANP2AHUtggBx2SEHcBMyxbyIa/WJcIOYIdlizjORtiBASsZ8X9/4JzGf3vohbeLzWPoq3WJsAOD0ibkbcJdZeyScR86wg4k1TTiXQZ81nnbxJ2V+nsIO5BEk5D3FfHSiPp2hB1YUnVD3ibib73flY47+FI0PkdTRP1shB1YEl2GvGq4q47TJPB1t2EI+mSEHVhQdUJeNeKlAl7lPHXiTtTLIuzAAqka8yohn1fE26oTdYJeDWEHetRXyN9+3zuVj5Wkc17eW+v4qqpGnaDXQ9iBOSsR8yoRrxvvKmNVDfysbRiC3i3CDnRsHiEvGfG2SkSdoLdD2IEOVIl505A3ifiR1Tf+//Op0xfU/ntp9mqdoC8Owg4U0HfIt4a7zrFNI7/TtKgT9Pkj7EBDXcV8WsjrBLyUaSt1gr6YCDtQw6yYZwj5VpOiTtAXG2EHZigd80khrxPx6y567qznTrx2aeW/n6WLoBPz+SHswA5ttljqrMpnhXxcvKscXyXwk/bWCXoORcJu+3pJ35W0S9I9EfGNEuMC81I65k1W5XVD3lSdqE8KOtsti6112G3vkvR9SddJOi3pMdu/john2o4NdGkeMZ8U8q4iPm21Pi7odVforM6XQ4kV+5WSno+IFyXJ9n2SbpRE2LFwmu6Xl9hi6XpFPinqBH14SoT9YkmvbHl8WtLHCowLFFEy5l2H/PPnntTP3/xorb9pG3Rins/cXjy1vSZpTZL2rRyY12kxUIsc88+fe/Ks5zZjXifqBB2TlAj7q5IOb3m8uvHcNhGxLmldkg7tuXD+t1lBek33zNvEfFbIx0V80nFVoz4u6MQcW5UI+2OSPmT7Eo2C/kVJNxUYF6ikyeq8y5V51ZjXVTrovLMlr9Zhj4gztm+T9AeN3u7444h4uvXMgCm63GqZZ8xnrdJZnaOJInvsEfFbSb8tMRYwSR/75l2tzKcFvereOTHHJHzyFAtt0WIuLc/qnJgPF2HHQlq0rRapWdDZakEfCDsWxiK/RVEaRXpW3Ku8s4WYo2uEHb3q62P9dT48NOmtiG3enigRc3SHsKMXXa/OpfZB37Q14MQcy4CwY276/NItqdvvauF7WrBICDs6twg3qugi6n2tyiVijukIOzozj29SlMrfsGKcul+HKxFz9Iewo6h53X1I6u5+oLPuQFTq7kPEHF0h7ChinkGX6kW97b1AJ4VcIuZYTIQdrXQRdKlc1Jsg5Fh2hB21VYm5VD7om06dvqBY3KdFXOrm5s4SMUe3CDsqaxt0qX3Um5oV8E2TQi4RcywPwo6Zug56E1VDPc20iEuEHMuLsGOiEkGXqkW9y9X6pq5DLhFzLAbCjrOUCrpUfqVexayAS9MjLhFyLDfCjv+rGnSpfNS3xnjW6r1KuHeaFXKJmCMPwg5J5aPeRpNwb1Uy4hIhx/Ih7AO3SEFvokrEJUKOYSHsA1Un6IugasA3EXIMGWEfoCZRb7JarxvjpupEfBMxR2aEfUCWbZU+DhEHZiPsA7GMUW8S8U3EHENG2AegRNQPvfB2Zy+etgm4RMSBnQh7ciVX6psBrhv4tuHeiZAD0xF21FY61NMQcaA+wp7Ysu2rE3GgDMKOXhBxoDuEHZ0i4MD8EfbENqM6jy0ZAg4sDsI+AFuj2yTyRBtYLoR9YIg0kN9K3xMAAJRF2AEgGcIOAMm0Crvtb9p+zvZfbP/S9nmlJgYAaKbtiv2EpA9HxEck/V3S3e2nBABoo1XYI+KBiDiz8fARScv1GXYASKjkHvutkn5XcDwAQAMz38du+0FJF4351fGI+NXGMcclnZF075Rx1iStSdK+lQONJgsAmG1m2CPi2mm/t32LpGOSromIiTe5jIh1SeuSdGjPhfO5GSYADFCrT57avl7SXZI+GRH/KTMlAEAbbffYvyfpoKQTtp+0/cMCcwIAtNBqxR4RHyw1EQBAGXzyFACSIewAkAxhB4BkCDsAJEPYASAZwg4AyRB2AEiGsANAMoQdAJIh7ACQDGEHgGQIOwAkQ9gBIBnCDgDJEHYASIawA0AyhB0AkiHsAJAMYQeAZAg7ACRD2AEgGcIOAMkQdgBIhrADQDKEHQCSIewAkAxhB4BkCDsAJEPYASAZwg4AyRB2AEiGsANAMoQdAJIh7ACQDGEHgGSKhN32nbbD9vklxgMANNc67LYPS/q0pJfbTwcA0FaJFfu3Jd0lKQqMBQBoqVXYbd8o6dWIeKrQfAAALe2edYDtByVdNOZXxyV9XaNtmJlsr0lak6R9KwdqTBEAUMfMsEfEteOet325pEskPWVbklYlnbR9ZUS8NmacdUnrknRoz4Vs2wBAR2aGfZKI+KukCzcf2z4l6WhE/LPAvAAADfE+dgBIpvGKfaeIOFJqLABAc6zYASAZwg4AyRB2AEiGsANAMoQdAJIh7ACQDGEHgGQIOwAkQ9gBIBnCDgDJEHYASIawA0AyhB0AkiHsAJAMYQeAZAg7ACRD2AEgGUfM/77Stt+Q9NLcT3y28yVxj9YRrsV2XI/tuB7v6fNavD8iLph1UC9hXxS2H4+Io33PYxFwLbbjemzH9XjPMlwLtmIAIBnCDgDJDD3s631PYIFwLbbjemzH9XjPwl+LQe+xA0BGQ1+xA0A6hH2D7Ttth+3z+55LX2x/0/Zztv9i+5e2z+t7Tn2wfb3tv9l+3vbX+p5PX2wftv2Q7WdsP2379r7ntAhs77L9Z9u/6XsukxB2jf4BS/q0pJf7nkvPTkj6cER8RNLfJd3d83zmzvYuSd+X9BlJl0n6ku3L+p1Vb85IujMiLpP0cUlfGfC12Op2Sc/2PYlpCPvItyXdJWnQLzhExAMRcWbj4SOSVvucT0+ulPR8RLwYEe9Iuk/SjT3PqRcR8Y+IOLnx81saxezifmfVL9urkj4n6Z6+5zLN4MNu+0ZJr0bEU33PZcHcKul3fU+iBxdLemXL49MaeMwkyfYRSVdIerTfmfTuOxotAt/teyLT7O57AvNg+0FJF4351XFJX9doG2YQpl2LiPjVxjHHNfrf8HvnOTcsJtsHJN0v6Y6IeLPv+fTF9jFJr0fEE7Y/1fd8phlE2CPi2nHP275c0iWSnrItjbYeTtq+MiJem+MU52bStdhk+xZJxyRdE8N8L+yrkg5veby68dwg2d6jUdTvjYhf9D2fnl0l6Qbbn5W0T9K5tn8aEV/ueV5n4X3sW9g+JeloRAzyy45sXy/pW5I+GRFv9D2fPtjerdELx9doFPTHJN0UEU/3OrEeeLTa+Ymkf0XEHX3PZ5FsrNi/GhHH+p7LOIPfY8c235N0UNIJ20/a/mHfE5q3jRePb5P0B41eLPzZEKO+4SpJN0u6euPfw5Mbq1UsOFbsAJAMK3YASIawA0AyhB0AkiHsAJAMYQeAZAg7ACRD2AEgGcIOAMn8D8ZDxBUcCg2mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import multivariate_normal\n",
    "x, y = np.mgrid[-5:5:.1, -5:5:.1]\n",
    "pos = np.empty(x.shape + (2,))\n",
    "pos[:, :, 0] = x; pos[:, :, 1] = y\n",
    "rv = multivariate_normal([0.5, -0.2], [[2.0, 0.9], [0.9, 0.5]])\n",
    "plt.contourf(x, y, rv.pdf(pos))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References:\n",
    "\n",
    "1. Roger Labbe's [repo](https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python) on Kalman Filters. (Majority of the examples in the notes are from this)\n",
    "\n",
    "\n",
    "\n",
    "2. Probabilistic Robotics by Sebastian Thrun, Wolfram Burgard and Dieter Fox, MIT Press.\n",
    "\n",
    "\n",
    "\n",
    "3. Scipy [Documentation](https://scipython.com/blog/visualizing-the-bivariate-gaussian-distribution/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  },
  "pycharm": {
   "stem_cell": {
    "cell_type": "raw",
    "source": [],
    "metadata": {
     "collapsed": false
    }
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}